Accepted Manuscript

Exergy Analysis of Parabolic Trough Solar Receiver

Ricardo Vasquez Padilla, Armando Fontalvo, Gokmen Demirkaya, Arnold Martinez,Arturo Gonzalez Quiroga

PII: S1359-4311(14)00232-4

DOI: 10.1016/j.applthermaleng.2014.03.053

Reference: ATE 5502

To appear in: Applied Thermal Engineering

Received Date: 15 November 2013

Revised Date: 7 March 2014

Accepted Date: 22 March 2014

Please cite this article as: R. Vasquez Padilla, A. Fontalvo, G. Demirkaya, A. Martinez, A. GonzalezQuiroga, Exergy Analysis of Parabolic Trough Solar Receiver, Applied Thermal Engineering (2014), doi:10.1016/j.applthermaleng.2014.03.053.

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service toour customers we are providing this early version of the manuscript. The manuscript will undergocopyediting, typesetting, and review of the resulting proof before it is published in its final form. Pleasenote that during the production process errors may be discovered which could affect the content, and alllegal disclaimers that apply to the journal pertain.

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

6sgssssssssssy ssssssssssssssssssssssss%ss sss2gssCssss sc%Casssssssssssssssssssssss%sssss s

s=smshs=svsh

1s=s(vms&hDHsss=sDmmsW

*scp

a

m

bm

Dm

um

Fm

vm

dm

(m

,12

6 2 ,2

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Highlights

A comprehensive exergy balance of a parabolic trough is performed

The thermal and exergy efficiency showed an opposite trend

The highest exergy destruction takes place at the absorber

The highest exergy losses is due to optical errors

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Exergy Analysis of Parabolic Trough Solar Receiver

Ricardo Vasquez Padillaa,∗, Armando Fontalvoa,1, Gokmen Demirkayab,2, Arnold Martineza,3, ArturoGonzalez Quirogaa,4

aDepartment of Mechanical Engineering, Universidad del Norte, Barranquilla, Colombia

bClean Energy Research Center, University of South Florida, 4202 E. Fowler Av. ENB 118 Tampa, Fl 33620

Abstract

∗Corresponding author. Assistant Professor. Department of Mechanical Engineering. Universidad del Norte, BarranquillaColombia, Km 5 Via Antigua Pto Colombia. Phone: (57) 5 3509272, Fax: (57) 5 3509255.

Email address: rvasquez@uninorte.edu.co (Ricardo Vasquez Padilla)1aefontalvo@uninorte.edu.co2gdemirka@mail.usf.edu3arnoldg@uninorte.edu.co4arturoq@uninorte.edu.co

Preprint submitted to Applied Thermal Engineering March 7, 2014

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

This paper presents an exergy analysis to study the effects of operational and environmental parameters on

the performance of Parabolic Trough Collectors. The exergyanalysis is based on a previous heat transfer

model published by the authors. The main parameters considered for the analysis are: inlet temperature and

mass flow rate of heat transfer fluid, wind speed, pressure or vacuum in annulus and solar irradiance. The

results showed that inlet temperature of heat transfer fluid, solar irradiance, and vacuum in annulus have

a significant effect on the thermal and exergetic performance, but the effect of wind speed and mass flow

rate of heat transfer fluid is negligible. It was obtained that inlet temperature of heat transfer fluid cannot

be optimized to achieve simultaneously maximum thermal andexergetic efficiency because they exhibit

opposite trends. Finally, it was found that the highest exergy destruction is due to the heat transfer between

the sun and the absorber while for exergy losses is due to optical error.

Keywords: Solar receiver, parabolic trough, exergy analysis

1. Introduction

Solar Parabolic Trough Collectors (PTCs) are currently used for electricity generation and applications

with temperatures up to 400 °C [1]. PTCs concentrate solar radiation onto a focal line to transform it into

useful energy by increasing the temperature of a Heat Transfer Fluid (HTF). The performance of PTCs

depends on the combination of several operation parametersunder different meteorological conditions. In

this context, this paper presents an exergy analysis to determine the performance of PTCs in terms of work

potential and location, type, and magnitude of exergy losses.

This research is based on a detailed and validated heat transfer model [2] that takes into account all heat

transfer mechanism among collector components and includes the thermal interaction with the environment.

Results of the heat transfer model are in excellent agreement with experimental data obtained at Sandia

National Laboratory [3], and also showed improvements whencompared with prior models [4, 5].

2

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Most of the previous research on exergy analysis of PTCs has been focused on heat and power production

systems. In these systems, the exergy analysis is used either to find optimal operation conditions or to

evaluate the performance of the system [6–13]. Some applications involve the optimization of the coupling

conditions between the heat transfer fluid and the power cycle [6–8]. Other applications have used the exergy

analysis to minimize the use of fossil fuels in polygeneration units [9–13]. Exergy analysis has also been

used in desalination processes that rely on thermal solar power obtained from PTCs [14, 15]. It is important

to highlight that in this last application, PTCs are only a component of the system under analysis, and what

it is optimized is the coupling between PTCs in the solar fieldwith the thermal desalination system.

Some studies on exergy analysis of PTCs have been focused on the performance evaluation of the col-

lectors to maximize the use of the incoming solar energy. Previous studies have reported the dependence

of exergy efficiency on the length of the collector and HTF temperature [16]; the influence of mass flow

of HTF, solar intensity and concentration ratio on energy and exergy efficiencies [17]; and the effect of

the collector length, absorber tube diameter, working temperature and pressure on the energy and exergy

efficiencies [18].

In this paper, a comprehensive exergetic balance of a PTC based on a control volume analysis is per-

formed. This analysis is based on a previous heat transfer model developed by the authors [2]. This analysis

shows the effect of inlet temperature and mass flow rate of theheat transfer fluid, solar irradiance, annulus

condition (vacuum or air) and wind speed on the thermal and exergetic performance of the PTC. The exer-

getic balance is very useful to identify the irreversibility sources which can be used to redesign and improve

the thermal performance of PTCs.

2. Solar Receiver Model

The solar receiver consists of a heat collection element composed of a stainless steel tube with a selective

absorber surface, which has high values of absorptance and low values of emittance for the temperature range

of operation. Most of the incoming solar radiation has wavelengths below 3µm which reduces the radiation

3

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

losses because of the emittance of the absorber [19]. The stainless tube is covered by an evacuated glass

tube (glass envelope) which prevents oxidation and minimizes the heat losses to the environment. Glass to

metal seals and metal bellows are employed to achieve the vacuum inside the envelope and compensate the

thermal expansion difference [20]. Bellows also allow extending the absorber to extend beyond the glass

envelope so that the HCE can form a continuous receiver (see Fig. 1).

The heat transfer model is an energy balance between the heattransfer fluid and its surroundings. Figure

2 shows the heat transfer resistance model in a cross sectionof the HCE. Readers are encouraged to consult

the details and assumptions of the heat transfer model developed by the authors in Ref. [2]. The heat

transfer model was compared with experimental data obtained from Sandia National Laboratory (SNL) [3]

and compared with other solar receiver models [4, 5]. Experimental results used in the model validation

were taken from LS-2 module placed at the AZTRAK rotating platform located at the SNL.

3. Exergy Analysis Model

An exergy balance was applied to the control volume shown in Figure 1. It should be noted that the same

assumptions of the heat transfer model are used. The partialdifferential equation of the exergy balance is as

follows [21]:

dEcv

dt= ∑

j

Eq j −Wcv +∑i

mi e f i −∑e

me e f e − Ed − Eloss (1)

with:

Eq j =

(

1−To

Tj

)

Q j (2)

e f = h−ho −To (s− so)+V 2

2+g z (3)

4

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

3.1. Exergy input

The exergy input includes the exergy inflow rate coming from the heat transfer fluid and the exergy of

the solar radiation. The total exergy input is:

Ei = m

[ˆ Ti

To

Cp (T ) dT +ν (Pi −Po)−To

ˆ Ti

To

Cp (T )

TdT +

V 2i

2

]

+ Ib Aa ψ (4)

For an ideal process, the relative potential of the maximum useful work available from radiation,ψ , is

calculated with Petela’s formula[22]:

ψ = 1−43

To

Ts+

13

(

To

Ts

)4

(5)

whereTs is the equivalent temperature of the sun as a black body (∼5800 K). Parrot [23] introduced the

effect of the sun’s cone angle (δ ∼0.005 rad) on the limiting efficiency for utilization of solar energy, the

expression obtained was:

ψ = 1−43

To

Ts(1−cosδ )1/4+

13

(

To

Ts

)4

(6)

3.2. Exergy Output

The exergy output only includes the exergy outflow rate coming from the heat transfer fluid exiting the

solar receiver. The total exergy output is as follows:

Ee = m

[ˆ Te

To

Cp (T ) dT +ν (Pe −Po)−To

ˆ Te

To

Cp (T )T

dT +V 2

e

2

]

(7)

The exergy gained by the heat transfer due to the incident radiation on the solar collector is given by :

Egain = m

[ˆ Te

Ti

Cp (T ) dT −To

ˆ Te

Ti

Cp (T )

TdT −ν ∆P

]

(8)

where the first two terms represent the exergy gain as result of an increase in the heat transfer fluid temper-

ature due to the solar insolation and flow friction and the last term represents the decrease of mechanical

5

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

energy due to flow friction. The exergy efficiency is defined asthe ratio of gain exergy to solar radiation

exergy:

ηex =Egain

Esr(9)

then:

ηex =

m

[

´ Te

TiCp (T ) dT −To

´ Te

Ti

Cp (T )T

dT −ν ∆P

]

Ib Aa ψ(10)

The last equation does not present the terms of loss and destroyed exergy which are useful to identify

the causes and location of thermal losses. The exergy lossesinclude heat transfer losses to the surround-

ings while the exergy destruction is caused by internal irreversibilities [24]. For steady state conditions

(dEcv/dt = 0), Eq. (10) can be rewriten as:

ηex = 1−Ed + Eloss

Ib Aa ψ(11)

3.3. Exergy Losses

In this paper exergy losses are due to optical error and heat transfer losses from the solar receiver to the

ambient [25].

Eloss = Eloss,opt + Eloss,q, (12)

The exergy leakage due to optical errors is as follows :

Eloss,opt = (1−ηo) Ib Aa ψ (13)

ηo is defined as the optical efficiency of the solar collector. The exergy loss due to heat transfer from

6

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

absorber to the ambient is given by [25]:

Eloss,q = ∑i

ˆ Ta,i

To

Qi,lossTo

T 2 dT (14)

whereQi,loss are the thermal losses. Simplifying:

Eloss,q = ∑j

Q j,loss

(

1−To

Ta, j

)

(15)

3.4. Exergy Destruction

In the solar receiver, exergy destruction is caused by two mechanism: friction of the viscous fluid (HTF) and

heat transfer from high to low temperatures [25]. The friction of the heat transfer fluid generates a pressure

drop through the solar receiver. The entropy generation (exergy destruction) during this process is as follows

[21]:

Ed,∆P = To m f ∑j

∆Pj

ρ j

ln (Te, j/Ti, j)

Te, j −Ti, j(16)

Exergy destruction due to heat transfer process is present on the absorber surface. The first process is the

heat transfer from the sun to the absorber surface, in this case the entropy generation is given by [26]:

Ed,q1 = ηo Ib Aa ψ −∑j

ηo I′

b ∆z Aa

(

1−To

Ta, j

)

(17)

The second heat transfer process is between the absorber andthe HTF. The exergy destruction by heat

conduction from the absorber to the fluid is [25]:

Ed,q2 = To m f

[

ˆ Te

Ti

Cp (T )dTT

−∑j

1Ta, j

ˆ Te, j

Ti, j

Cp (T ) dT

]

(18)

Then, the total exergy destruction is:

Ed = Ed,∆P + Ed,q1+ Ed,q2 (19)

7

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Replacing all terms Eq. (13)-(18), the exergy efficiency canbe rewriten by introducing dimensionless exergy

term (E ′ = E/Esr):

ηex = 1−(

E ′d,∆P + E ′

d,q1+ E ′d,q2+ E ′

loss,opt + E ′loss,q

)

(20)

with:

E ′loss,opt = (1−ηo) (21)

E ′loss,q =

∑ j Q j,loss

(

1−To

Ta, j

)

Ib Aa ψ(22)

E ′d,∆P = To m f

∑ j∆Pj

ρ j

ln (Te, j/Ti, j)

Te, j −Ti, j

Ib Aa ψ(23)

E ′d,q1 = ηo

[

1+1ψ

(

∆zLc

∑j

To

Ta, j−1

)]

(24)

E ′d,q2 = To m f

´ TeTi

Cp (T )dTT

−∑ j1

Ta, j

´ Te, jTi, j

Cp (T ) dT

Ib Aa ψ(25)

4. Results and discussion

A parametric study was performed by using a LS-3 parabolic trough solar collector in order to study

the effect of some operating and environmental parameters on the collector efficiency and collector exergy

efficiency. The geometrical parameters of the LS-3 collector are listed in Table 1. The variations of exergy

leakages and exergy destruction with these parameters werealso studied. Table 2 shows the operating

conditions used for the parametric analysis.

8

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Figure 3 to 8 shows the effect of HTF inlet temperature(Ti), mass flow rate(m) and solar irradiance(Ib)

on Collector Efficiency(ηc)and Collector Exergy Efficiency(ηex). Collector Exergy Efficiency is strongly

dependent on HTF inlet temperature. This result may be explained by the influence of exergy leakage due to

thermal losses, and exergy destruction due to heat transferfrom the sun to the absorber, which are strongly

dependent of HTF temperature. According to Figures 3 to 6, anincrease in the HTF inlet temperature leads

to a significant increase in Collector Exergy Efficiency, butit causes a reduction in Collector Efficiency.

When HTF inlet temperature increases, Collector Efficiencyshows an average reduction of 15.5% and 7.6%

for irradiance levels of 250 and 500 W/m2 respectively according to Figures 3 and 4, whereas the average

reduction of Collector Efficiency for irradiances of 750 and1000 W/m2 are 4.7% and 3.25% respectively,

as it is shown in Figures 5 and 6.

On the other hand, Figures 3 and 4 showed an average increase of 6.9% and 7.9% in Collector Exergy

Efficiency for solar irradiance levels of 250 and 500 W/m2, respectively. For high solar irradiance, according

to Figures 5 and 6, the average increase was 7.3% and 7.7% for solar irradiance of 750 and 1000 W/m2,

respectively. The maximum Collector Exergy Efficiency, under vacuum condition, was between 30.3% and

36.6%, for irradiance levels of 250 W/m2and 1000 W/m2, respectively. Results described above allows to

conclude that in days with low irradiance levels(

250−500W/m2)

the increase of HTF inlet temperature

to achieve maximum Collector Exergy Efficiency would significantly penalize the Collector Efficiency, but

in days with high irradiance levels(

750−1000W/m2)

the maximum or near maximum Collector Exergy

Efficiency can be achieved with a less severe impact on Collector Efficiency. However, it is clear that a

simultaneous maximization of both efficiencies is not possible by just adjusting the HTF inlet temperature.

This opposite trend of Collector Efficiency and Collector Exergy Efficiency is explained by the behavior of

the exergy destruction due to heat transfer between the absorber and the HTF, and the thermal losses due to

heat transfer from absorber to the environment. An increasein HTF inlet temperature would increase the

thermal losses and a decrease in exergy destruction due to heat transfer between the absorber and the HTF,

9

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

as it can be seen in Figures 9 and 10, causing a decrease in Collector Efficiency and an increase in Collector

exergy Eficiency.

The optimum operating conditions for PTCs can be assessed bymeans of collector efficiency analysis

and collector exergy efficiency analysis. The common aim is to optimize the thermal efficiency of any

collector, which is defined as the ratio of ‘useful energy output’ to that of ‘incident solar energy’ during

the same time period. In this work, the performance of PTCs isexamined from the standpoint of exergy,

which is a useful method to complement, not to replace the energy analysis. Exergy analysis quantifies

the collection and useful consumption of exergy and pinpoints the unrecoverable losses, leading the way

to improve the system. Results show that collector efficiency and collector exergy efficiency are increasing

functions of mass flow rate for a given value of solar intensity. On the other hand, for low values of solar

intensity(

I < 500W/m2)

and a given mass flow rate, collector exergy efficiency exhibits a maximum as

inlet temperature increases. Collector efficiency is a decreasing function of inlet temperature over the whole

solar intensity range studied(

100W/m2 < I < 1000W/m2)

. However the influence of inlet temperature

on collector efficiency significantly diminishes at high solar intensities.

The effect of wind speed and vacuum in annulus on both Collector Efficiency and Collector Exergy

Efficiency is shown in Figure 7 to 10. According to Figures 7 and 8, results indicate that vacuum in annulus

reduces the effect of wind speed because both efficiencies showed no significant variation with wind speed.

However, in absence of vacuum, the increase of wind speed leads to average reductions of 5% and 4%

for Collector Efficiency and Collector Exergy Efficiency, respectively. According to Figures 9 and 10,

when pressure in annulus is below 1 Torr, convective heat transfer inside the annulus is not significant,

consequently its contribution to the exergy loss due to heattransfer from absorber to the surroundings is

also reduced. On the other hand, if pressure in annulus is above 1 Torr, convective heat transfer inside the

annulus is increased thereby increasing its contribution to the exergy loss due to heat transfer from absorber

to the surroundings, which is the exergy waste that can be affected by the wind speed.

10

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

For mass flow rate, Figure 3 to 6 shows that both Collector Efficiency and Collector Exergy Efficiency

have small variations with mass flow rate and the optimum value for both efficiencies was practically the

same for the three mass flow rates considered. Figures 11 to 12show that exergy losses and exergy destruc-

tion are almost independent from mass flow rate because exergy destruction due to the friction of the HTF

and heat transfer between the absorber and the HTF are the ones that have a noticeable variation with mass

flow rate, but their contribution to the total exergy losses and destruction is less than 0.5%.

Figures 9 and 10 illustrate the effect of HTF inlet temperature on the exergy destruction due to heat

transfer between the sun and the absorber. This exergy destruction accounts for 35% to 40% of the to-

tal exergy wasted. When HTF inlet temperature increases, the exergy destruction diminishes because the

temperature difference is lower. However, the exergy losses to the surroundings increase as the HTF inlet

temperature raises as a consequence of the temperature difference. The combine effect of exergy destruction

due to heat transfer between the sun and the absorber and exergy losses to the surroundings is accountable

for an optimum exergy efficiency point. After this point is reached, exergy losses to surroundings accounts

for 5% to 10% of the total exergy wasted and increase more rapidly than the decrease of exergy destruction

due to heat transfer.

5. Conclusions

An exergy analysis of parabolic trough solar receiver was carried out based on a heat transfer model

proposed by the authors. The performance of the solar receiver was simulated for a fixed values of solar

irradiance, HTF mass flow rate, HTF inlet temperature, with and without vacuum in annulus, and with

presence and absence of wind. Based on the results obtained,the following conclusions are proposed:

• Current results are useful to improve the design of PTCs andcompare performances between PTCs

options. However operating conditions are also determinedby others factors beyond exergy analysis

of the collector like collector area, which impacts capitalcosts as the fuel (sunlight is free), and

pumping power at increasing mass flow rates.

11

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

• HTF inlet temperature has a significant effect on CollectorEfficiency and Collector Exergy Efficiency.

HTF inlet temperature affects the exergy leakage due to thermal losses, and exergy destruction due to

heat transfer from the sun to the absorber.

• Solar Irradiance has a significant effect on the performance of the parabolic trough solar receiver.

High solar irradiances allows to work at higher HTF inlet temperatures, which leads to high values of

Collector Exergy Efficiency with a negligible reduction of the Collector Efficiency.

• The optimal performance of PTC is independent from the massflow rate, since exergy destruction

due to friction of the heat transfer fluid and heat transfer between the absorber and the HTF depends

on mass flow rate, but their contribution to the total exergy wasted is less than 0.5%.

• The performance of the solar receiver is strongly dependent on vacuum in annulus. Vacuum in annulus

mitigates the effect of wind speed, but its absence increases the thermal losses to the surroundings,

which leads to a reduction of both Collector Efficiency and Collector Exergy Efficiency.

6. References

References

[1] A. Fernández-García, E. Zarza, L. Valenzuela, M. Pérez,Parabolic-trough solar collectors and theirapplications, Renewable and Sustainable Energy Reviews 14(7) (2010) 1695–1721.

[2] R. V. Padilla, G. Demirkaya, D. Y. Goswami, E. Stefanakos, M. M. Rahman, Heat transfer analysis ofparabolic trough solar receiver, Applied Energy 88 (12) (2011) 5097 – 5110.

[3] V. Dudley, G. Kolb, M. Sloan, D. Kearney, SEGS LS2 Solar Collector-Test Results, Report of SandiaNational Laboratories, SAN94-1884, 1994.

[4] R. Forristall, Heat Transfer Analysis and Modeling of a Parabolic Trough Solar Receiver Implementedin Engineering Equation Solver, National Renewable EnergyLaboratory (NREL), Colorado, 2003.

[5] O. García-Valladares, N. Velázquez, Numerical simulation of parabolic trough solar collector: Im-provement using counter flow concentric circular heat exchangers, International Journal of Heat andMass Transfer 52 (3-4) (2009) 597–609.

[6] M. Kane, D. Favrat, K. Ziegler, Y. Allani, Thermoeconomic analysis of advanced solar-fossil combinedpower plants, International Journal of Thermodynamics 3 (4) (2010) 191–198.

[7] Y. You, E. J. Hu, A medium-temperature solar thermal power system and its efficiency optimisation,Applied thermal engineering 22 (4) (2002) 357–364.

12

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

[8] N. Singh, S. Kaushik, R. Misra, Exergetic analysis of a solar thermal power system, Renewable energy19 (1) (2000) 135–143.

[9] G. Song, H. Hongjuan, Y. Yongping, Optimize on the temperature of solar collectors in solar aidedcoal-fired electric generation, in: Sustainable Power Generation and Supply, 2009. SUPERGEN’09.International Conference on, IEEE, 2009, pp. 1–4.

[10] H. Zhai, Y. Dai, J. Wu, R. Wang, Energy and exergy analyses on a novel hybrid solar heating, coolingand power generation system for remote areas, Applied energy 86 (9) (2009) 1395–1404.

[11] A. Baghernejad, M. Yaghoubi, Exergy analysis of an integrated solar combined cycle system, Renew-able Energy 35 (10) (2010) 2157–2164.

[12] V. S. Reddy, S. Kaushik, S. Tyagi, Exergetic analysis and performance evaluation of parabolic troughconcentrating solar thermal power plant (ptcstpp), Energy39 (1) (2012) 258–273.

[13] F. A. Al-Sulaiman, I. Dincer, F. Hamdullahpur, Exergy modeling of a new solar driven trigenerationsystem, Solar Energy 85 (9) (2011) 2228–2243.

[14] A. Nafey, M. Sharaf, Combined solar organic rankine cycle with reverse osmosis desalination process:Energy, exergy, and cost evaluations, Renewable Energy 35 (11) (2010) 2571–2580.

[15] M. Sharaf, A. Nafey, L. García-Rodríguez, Exergy and thermo-economic analyses of a combined solarorganic cycle with multi effect distillation (med) desalination process, Desalination.URL http://www.scopus.com/inward/record.url?eid=2-s2.0-79952628903&partnerID=40&md5=6a49dcc3e4c2d049155aa537f534cac2

[16] R. RT, Exergic efficiency of solar thermal units with linear concentrators, Applied Solar Energy 41 (1)(2005) 24–28.

[17] S. Tyagi, S. Wang, M. Singhal, S. Kaushik, S. Park, Exergy analysis and parametric study of concen-trating type solar collectors, International journal of thermal sciences 46 (12) (2007) 1304–1310.

[18] M. Montes, A. Abánades, A.nades, J. Martinez-Val, Thermofluidynamic model and comparative anal-ysis of parabolic trough collectors using oil, water/steam, or molten salt as heat transfer fluids, Journalof solar energy engineering 132 (2) (2010).

[19] D. Y. Goswami, F. Kreith, J. F. Kreider, F. Kreith, Principles of Solar Engineering, second ed., Taylor& Francis, Philadelphia, PA, 2000.

[20] H. Price, E. Lüpfert, D. Kearney, E. Zarza, G. Cohen, R. Gee, R. Mahoney, Advances in parabolictrough solar power technology, Journal of Solar Energy Engineering, Transactions of the ASME124 (2) (2002) 109–125.

[21] M. J. Moran, H. N. Shapiro, Fundamentals of EngineeringThermodynamics, Student Problem SetSupplement, 5th Edition, Wiley, 2004.

[22] R. Petela, Exergy of undiluted thermal radiation, Solar Energy 74 (6) (2003) 469–488.

[23] J. Parrott, Theoretical upper limit to the conversion efficiency of solar energy, Solar Energy 21 (3)(1978) 227–229.

[24] I. Dincer, M. A. Rosen, EXERGY: Energy, Environment andSustainable Development, Elsevier Sci-ence, 2007.

13

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

[25] A. Suzuki, General theory of exergy-balance analysis and application to solar collectors, Energy 13 (2)(1988) 153–160.

[26] A. Bejan, G. Tsatsaronis, M. Moran, Thermal design and optimization, Wiley-Interscience, 1996.

[27] F. Kreith, D. Y. Goswami, Handbook of Energy Efficiency and Renewable Energy, first ed., CRC,2007.

14

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Figure Captions

List of Figures

1 Parts of a heat collection element (HCE) and control volumeused for the heat transfer anal-

ysis. Adapted from [27] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . 16

2 Heat transfer and thermal resistance model in a cross section at the heat collection element

(HCE). (a) Heat Transfer, (b) Thermal circuit. Adapted from[3, 4] . . . . . . . . . . . . . . 17

3 Collector Efficiency and Collector Exergy Efficiency vs HTFinlet temperature for diferent

values of mass flow. I=250W/m2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4 Collector Efficiency and Collector Exergy Efficiency vs HTFinlet temperature for diferent

values of mass flow. I=500W/m2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5 Collector Efficiency and Collector Exergy Efficiency vs HTFinlet temperature for diferent

values of mass flow. I=750W/m2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

6 Collector Efficiency and Collector Exergy Efficiency vs HTFinlet temperature for diferent

values of mass flow. I=1000W/m2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

7 Collector Efficiency and Collector Exergy Efficiency vs HTFinlet temperature with and

without vaccum, for natural and forced convection. I=250W/m2 . . . . . . . . . . . . . . . 22

8 Collector Efficiency and Collector Exergy Efficiency vs HTFinlet temperature with and

without vaccum, for natural and forced convection. I=750W/m2 . . . . . . . . . . . . . . . 23

9 Dimensionless Exergy Losses vs Inlet Temperature. Conditions: m = 7kg/s; Vair = 0m/s

(Natural Convection); Without Vacuum. . . . . . . . . . . . . . . . . .. . . . . . . . . . . 24

10 Dimensionless Exergy Losses vs Inlet Temperature. Conditions: m = 7kg/s; Vair = 5m/s

(Forced Convection); Without Vacuum. . . . . . . . . . . . . . . . . . .. . . . . . . . . . 25

11 Dimensionless Exergy Losses vs Mass flow rate. Conditions: I = 750W/m2; Vair = 0m/s

(Natural Convection); Without Vacuum in annulus. . . . . . . . .. . . . . . . . . . . . . . 26

12 Dimensionless Exergy Losses vs Mass flow rate. Conditions: I = 750W/m2; Vair = 5m/s

(Forced Convection); Without Vacuum in annulus. . . . . . . . . .. . . . . . . . . . . . . 27

15

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Expansionbellows Glass EnvelopeAbsorber tubewithselective coating Vacuum betweenenvelope and absorberFigure 1: Parts of a heat collection element (HCE) and control volume used for the heat transfer analysis.Adapted from [27]

16

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Absorber pipe - a

Selective coating

Heat Transfer Fluid - f

Glass envelope - e

Surrounding air - sa

Sky - s_Qa¡f ;conv_Qcond¡bracket

_Qa¡abs _Qa¡e ;conv _Qa¡e;rad_Qe¡abs _Qe¡sa ;conv _Qe¡s ;rad

(a)

(b)

Figure 2: Heat transfer and thermal resistance model in a cross section at the heat collection element (HCE).(a) Heat Transfer, (b) Thermal circuit. Adapted from [3, 4]

17

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

l l l

(l/2l/7sl/

l

ll

li n

1s

11

1(

1)

16

0s

01

0(

0)

06

(s

l li n

1s

1%

0s

0%

(s

(%

%s

%%

)s

)%

2s

2%

l !"#$lin

7%s 1ss 1%s 0ss 0%s

Figure 3: Collector Efficiency and Collector Exergy Efficiency vs HTF inlet temperature for diferent valuesof mass flow. I=250W/m2

18

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

l l l

(l/2l/7sl/

l

ll

li n

1s

11

1(

1)

16

0s

01

0(

0)

06

(s

l li n

1s

1%

0s

0%

(s

(%

%s

%%

)s

)%

2s

2%

l !"#$lin

7%s 1ss 1%s 0ss 0%s

Figure 4: Collector Efficiency and Collector Exergy Efficiency vs HTF inlet temperature for diferent valuesof mass flow. I=500W/m2

19

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

l l l

4l/1sl/

l

ll

li n

0s

00

0%

02

06

(s

(0

(%

(2

(6

%s

l li n

0s

0)

(s

()

%s

%)

)s

))

2s

2)

4s

4)

l !"#$lin

1)s 0ss 0)s (ss ()s

Figure 5: Collector Efficiency and Collector Exergy Efficiency vs HTF inlet temperature for diferent valuesof mass flow. I=750W/m2

20

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

l l l

4l/1sl/

l

ll

li n

0s

00

0%

02

06

(s

(0

(%

(2

(6

%s

l li n

0s

0)

(s

()

%s

%)

)s

))

2s

2)

4s

4)

l !"#$lin

1)s 0ss 0)s (ss ()s

Figure 6: Collector Efficiency and Collector Exergy Efficiency vs HTF inlet temperature for diferent valuesof mass flow. I=1000W/m2

21

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

8lT 8lT lT

l1l=ldgll1l,ldgll1l=ldgl6l1l,ldgl6

8

lT

llT

li n

0,

m=

m,

/=

/,

s=

8lT li n

m=

m,

/=

/,

s=

s,

,=

,,

a=

a,

u=

u,

5=

'l()li8n

0,= m== m,= /== /,=

Figure 7: Collector Efficiency and Collector Exergy Efficiency vs HTF inlet temperature with and withoutvaccum, for natural and forced convection. I=250W/m2

22

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

8lT 8lT lT

l1l=ldgll1l,ldgll1l=ldgl6l1l,ldgl6

8

lT

llT

li n

0,

m=

m,

/=

/,

s=

8lT li n

m=

m,

/=

/,

s=

s,

,=

,,

a=

a,

u=

u,

5=

'l()li8n

0,= m== m,= /== /,=

Figure 8: Collector Efficiency and Collector Exergy Efficiency vs HTF inlet temperature with and withoutvaccum, for natural and forced convection. I=750W/m2

23

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

d2d2d2l d2nd2x

ll∆t

e

y

ne

ny

xe

xy

re

ry

ge

gy

ye

yy

(e

!l"#$l∆.

nye xee xye ree rye

e

ein

eix

eir

eig

eiy

nye xee xye ree rye

Figure 9: Dimensionless Exergy Losses vs Inlet Temperature. Conditions: ˙m = 7kg/s;Vair = 0m/s (NaturalConvection); Without Vacuum.

24

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

d2d2d2l d2nd2x

ll∆t

e

y

ne

ny

xe

xy

re

ry

ge

gy

ye

yy

(e

!l"#$l∆.

nye xee xye ree rye

e

ein

eix

eir

eig

eiy

nye xee xye ree rye

Figure 10: Dimensionless Exergy Losses vs Inlet Temperature. Conditions: ˙m = 7kg/s; Vair = 5m/s(Forced Convection); Without Vacuum.

25

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

d2d2d2l d2nd2x

7

ll∆t

y

ne

ny

xe

xy

re

ry

ge

gy

ye

yy

(e

(y

!"l#$l"l∆%m

g % ne

e2n

e2x

e2r

e2g

e2y

g % ne

Figure 11: Dimensionless Exergy Losses vs Mass flow rate. Conditions: I = 750W/m2; Vair = 0m/s(Natural Convection); Without Vacuum in annulus.

26

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

d2d2d2l d2nd2x

7

ll∆t

y

ne

ny

xe

xy

re

ry

ge

gy

ye

yy

(e

(y

!"l#$l"l∆%m

g % ne

e2n

e2x

e2r

e2g

e2y

g % ne

Figure 12: Dimensionless Exergy Losses vs Mass flow rate. Conditions: I = 750W/m2; Vair = 5m/s(Forced Convection); Without Vacuum in annulus.

27

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Table 1: Geometrical and optical data for the LS-3 ParabolicTrough collector. Adapted from [20].

Parameter Value

Aperture width (m) 5.76

Focal length (m) 1.71

Length per element (m) 12

Length per collector (m) 99

Receiver diameter (m) 0.07

Geometric concentration 82:1

Peak optical efficiency (%) 80

28

MANUSCRIP

T

ACCEPTED

ACCEPTED MANUSCRIPT

Table 2: Summary of the parameters assumed for the analysis.

Parameters Values Units

HTF Mass Flow Rate 4, 7, 10 kg/s

Solar Irradiance 250, 500, 750, 1000 W/m2

Wind Speed 0, 5 m/s

Vacumm in AnnulusP < 1Torr(Vacuum)P ≥ 1Torr(Pressure in annulus)

29